Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems

A practical design that combines a fuzzy adaptation technique with sliding mode control to enhance robustness and sliding performance in a class of uncertain MIMO nonlinear systems is proposed. Using an online adaptation scheme, a fuzzy sliding mode controller is used to approximate the equivalent control in the neighbourhood of the sliding manifold. The hitting control is appended to ensure that the fuzzy sliding mode control can achieve a stable closed-loop system for the trajectory-tracking control of a plant with unknown nonlinear dynamics. The proposed design simultaneously guarantees the stability of the adaptation of the fuzzy rules and obtains suitable equivalent control when the nominal mathematical model is unknown in advance. It also provides the designers with flexibility to design and implement the fuzzy rule base without domain experts and without a mathematical model. The robust adaptive scheme is applied to a two-link robotic manipulator and shown to be able to guarantee that the output tracking error will ultimately converge to a residual set.